function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters.

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta


J = sum(-y'*log(sigmoid(X*theta))-(1-y)'*log(1-sigmoid(X*theta)))/m + lambda / (2*m) * sum(theta(2:size(theta)(1)).^2)


grad(1) = sum((sigmoid(X*theta) - y)'*X(:,1))/m
for i = 2:size(theta)(1)
    grad(i) = sum((sigmoid(X*theta) - y)'*X(:,i))/m + (lambda/m) * theta(i)


% =============================================================

end
